While RSI is a much weaker condition than convexity, at a high level, it assumes that the gradients of \(\mathrm {Err}_{n} (*)\)  are informative about the error in the parameter space \( *\) . We can further relax this assumption. In this section, we consider a weakening of this assumption which only supposes that \(\mathrm {Err}_{n} (*)\)  grows at least quadratically in \(\Vert   * \Vert _2\) . This is known as the quadratic growth (QG) condition [1]}. This condition no longer characterizes the behavior of the gradients of the function \(\mathrm {Err}_{n} (*)\) , much less those of the empirical loss \(\mathcal {L}_n\) . Stationary points of a function satisfying the QG condition are no longer global minima, in contrast with the behavior under the RSI (def:RSI).
